unless we have this guide to assist in tracing what the principle of uniformity is in any particular case Without such assistance, we may go on collecting and observing a vast number of facts, and yet arrive at no conclusions, or only at such as are altogether empty and visionary.

As we have already remarked, that merely to affirm what we observe in common of a number of individuals, all of which are before us, is hardly worthy the name of an induction, so it is a violation of all just induction to infer a general property from too limited a number of instances. But what constitutes the sufficient number of instances must depend on the nature of the case, and the experience and power of judgment possessed by the inquirer.

And if we fall into the error of too small an induction, the usual cause of such error is rather that the induction is wanting in a just principle of probability in our first conjecture, or that we have proceeded on the supposition of a wrong sort of relation. It is this which has commonly much more to do with the justness of our conclusion than the mere number of instances collected. And, on the other hand, it often happens that a very few instances, or even almost a single instance, have been admitted without question as a sufficient verification: but this has depended entirely on the justness of the assumed relation.

We will illustrate these remarks by a few examples, both of successful and unsuccessful inductions, in different departments of science.

1. Newton, on passing a ray of light through a prism of glass, found it separated into coloured rays; and measuring the proportion in which it is thus spread out, or " dispersed," announced that proportion as the general law of prismatic dispersion.

Dr. Lucas repeated the experiment; but assigned a much less proportion as the law. Both parties positively maintained the correctness of their respective conclusions. But they had both argued on a faulty ground of induction: they had each taken for granted that their prisms ought to act equally on light. The fact was, they had used different sorts of glass, which vary considerably in dispersive power.

This is remarkable as one of the very few instances in which Newton failed in an induction; but such failures are instructive; for we learn to observe the reason of the error. It was manifestly from neglecting to consider, in this case, what probability there would be, previous to trial, that different sorts of glass should possess the same dispersive power.

On the other hand, Newton's capital result that "to the same ray ever belongs the same refrangibility," (the media being the same,) is a conclusion, indeed, of a most general nature, and which universal experience has amply confirmed, but it was founded on a very limited induction derived from prismatic experiments with, at most, three or four different media.

2. The early history of astronomy is full of

examples of the compatibility of accumulated observation with the want of satisfactory induction. The ancient astronomers were indefatigable in the diligence with which they amassed observations. But they constructed out of them no theory which could attain a real permanence. The system of Ptolemy sufficed to a certain extent to represent the observed motions of the planets. The advance in accuracy of observations, however, soon required corresponding improvements in the system; which was obliged to be modified to accord with them: but, at length, the immense complexity introduced by the cycles and epicycles which were necessary to account for the apparent motions, began to induce a persuasion that such complication could not be the real law of nature: juster principles were therefore to be sought. No astronomer ever laboured more sedulously in making and recording observations, than Tycho Brahe. But though persuaded of the insufficiency of the Ptolemaic hypothesis, he did not succeed in constructing a better: not from deficiency of facts, but from his strangely-erroneous assumption of a guiding theoretical principle.

Kepler worked upon Tycho's materials. The labour which he bestowed on calculation was absolutely incredible. But theory after theory was adopted and rejected, because he had not any other guide than random conjecture, and nothing but the accurate calculation of every detail could suffice to put those conjectures to the test. He had not

lighted on any happy ground of antecedent probability. When, however, at last, he did seize upon the true law of nature, the numerical verification was perfect and decisive; and when thus established in the single instance of the planet Mars, it is extremely instructive to observe the rapidity and facility with which the inference was extended to the whole solar system.

When the laws of the motion of one planet were established, a single conjecture sufficed to point out, with the highest degree of probability, the laws of all the other planetary orbits: and a single calculation to verify it. The difference was, that there was now a ground of antecedent probability; a presumption of a guiding resemblance, which (though not strictly proved) was yet such as to leave no doubt that it had some foundation in nature.

Analogy the Ground of antecedent Probability.

THUS, then, it is manifest, that to possess some reasonable ground of antecedent probability, as a guide to our conclusion, is absolutely essential to physical induction. And we cannot employ the term correctly in its higher sense, (as referring to anything above a mere collection of instances,) without meaning to include specially the notion of a fair presumption of some relation, in virtue of which we can argue from the known to the unknown; and infer that those cases which we do not see, are pro

bably connected with those which we do. This constitutes one most essential characteristic of the inductive process; and without it, assuredly we can never advance to a substantial conclusion. We must always, then, consider the inductive method as referring, not merely to the accumulation of instances, but as involving the idea of some presiding conception, some guiding principle, of presumed connexion and probable relation between the facts on which we are reasoning.

In replying, then, to the inquiry, What constitutes the ground of antecedent probability, so essential to a good induction? it will be almost apparent, from the examples already cited, that the main ground is that afforded by the comparison of one class of phenomena with another: the perception of a parallelism in their respective conditions: the existence of an ANALOGY between them.

The success, then, with which induction may be carried on, depends on the just appreciation of such trains of analogy. This can only be attained by a habit of cautiously comparing our presumed generalization with already established laws. One induction must be the guide to another. We must seek to interpret nature in agreement with her own principles already displayed. Every real natural truth, we may be assured, will be in harmony with other parts of the great series and scale of natural truth. With this our hypothesis must be in accordance; to ascertain and verify such accordance is the